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Results tagged with elliptic-pde
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user 123448
Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
11
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2
answers
811
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Is it possible to obtain the inequality $\|\nabla f\|_{L^{2p}} \leq C (\|f\|_{L^\infty} \|f\...
Nirenberg's paper On elliptic PDEs claims that if a function $f$ on $\mathbb{R}^n$ tends to zero at infinity or is in $L^q$ for any $q < \infty$ then the "interpolation" inequality
$$
\lVert∇ f \rVert …
- 1,141
1
vote
0
answers
41
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Deriving the general interior elliptic estimate from the compactly supported case
This is an exercise (10.3.4 in the third edition) from Nicolaescu's Lectures on the Geometry of Manifolds.
Let $L$ be an elliptic differential operator of order $k$ and $1 < p < \infty$. The book prov …
- 1,141
1
vote
0
answers
157
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Sobolev interpolation inequality for relatively compact subdomains
I was looking at Nicolaescu's Lectures on the Geometry of Manifolds (3rd edition). In Theorem 10.2.29 he presents (without proof) the following inequality:
For $m \geq 1, p \geq 1, 0 < r \leq R$ there …
- 1,141